The Iranians were not ready to have an encounter at the presidential level, the official said.
The White House was open to a meeting between Obama and Rohani in New York, but the Iranians indicated it was too complicated, the official said.
Rohani did, however, meet with with French President Francois Hollande. A picture of the two leaders was posted on Hollande's Twitter account.
He also met with International Monetary Fund chief Christine Lagarde for talks that focused on his government's economic policies and way to deepen relations with the international institution.
IMF spokesman Gerry Rice told Reuters the meeting, on the sidelines of UNGA meetings in New York, was at the request of the Iranian authorities "to discuss global economic developments, the government's economic priorities, and how the partnership with the IMF might be deepened."
It was their first meeting since Rohani took office in August, another sign that Rohani is seeking to smooth relations with the West and bring Iran fully back into the international fold.
He has agreed to renew long-stalled talks on Iran's nuclear program and will meet world powers at the UN later this week, and there are signs of a possible thaw in relations between Washington and Tehran after more than three decades of estrangement.
The IMF last visited Iran in 2011 to assess the state of its economy. The possibility of an IMF mission to Tehran will be discussed at upcoming meetings of the IMF and World Bank in Washington, Rice added.
An IMF mission would allow the Fund to take a closer look at the impact of Western sanctions and gather more accurate data on the economy. Sanctions have hurt trade and largely frozen Iran out of the international banking systems since late 2011. Analysts believe the country's oil exports have been roughly halved.
In April, the IMF forecast that Iran's gross domestic product would shrink 1.3 percent this year after contracting 1.9 last year. But the Fund forecast the Iranian economy would likely resume expanding in 2014 at a pace of 1.1 percent.
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